That won't happen. Your lights never stay on with the Fit. In fact, most modern cars now have this feature. Long time coming for some manufacturers, though. I think Subaru may have been an early adopter. I've had three Subarus, the earliest being a '84 GL-10 Coupe and I never had to turn the lights off on any of them.

 

there are sensitivity settings for the auto headlights and autodim of headunit, buried deep in the vehicle settings. not sure if "high/med/low" mean they are more or less sensitive, or take more or less time to turn on, or react to more or less light??? but adjusting those might help solve your issue.

 

+1 Yup, Manual mode, I have my 2015 EX 6 speed for 2+ years now and no issue with the battery yet.

 

Fit's battery can handle headlights being on all the time. Been running mine like that and I have a 2+ hour round trip commute and have 54k miles on it. Still have the original battery but will probably source the 51R for a future replacement.

 

Same here.
With older cars, before alternators, everything would be powered with the battery and the generator would recharge the battery on an ongoing basis.
Nowadays, the battery has nothing to do with the lights when the engine is running. All electricals runs directly off the alternator. The battery only comes into play when the engine is off. So there is no issue running full lights all the time. I always do - it's safer.